Question

The radius of Jupiter is 11 times the radius of the earth. Calculate the ratio of the volumes of Jupiter and the earth. How many earths can Jupiter accommodate .
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Answer 1

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Answer 2

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Let,

Radius of earth be R1 &

Radius of Jupiter be R2.

So,

according to the question the radius of the planet Jupiter is 11 times the radius of Earth it means that,

R2=11×R1

We are talking about the planets in the question so according to the need of question we need to apply the formula for the volume of the sphere because the planets are spherical in shape,

So,let V1 be the volume of planet Jupiter,

$\begin{gathered} \\ v_1(volume \: of \: jupiter) = \frac{4}{3}\pi \: {(11r)}^{3}..(here \: we \: are \: taking \: about \: the \: radius \: of \: jupiter = 11r ) \\ \\ v_1 = \frac{4}{3}\pi \: r^{3} \times 1331...(taking \: cube \: of \: 11) \\ \\ v_2 = (volume \: of \: earth) = \frac{4}{3} \pi \: {r}^{3}..(here \: we \: are \: talking \: about \: the \: radius \: of \: earth = r)\end{gathered}$

$\begin{gathered} \\ \frac{v_1}{v_2} = \dfrac{\frac{4}{3} \times r^3 \times 1331 }{ \frac{4}{3} \times r^3 }\\ \\ \frac{v_1}{v_2} = 1331..( \frac{4}{3} \pi {r}^{3} gets \: cancelled \: from \: the \: numerator \: as \: well \: as \: the \: denominator)\end{gathered}$

Therefore,

the number of earth that Jupiter can accommodate is 1331.

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